Run and hide: visual performance in a brittle star
Lauren Sumner-Rooney1*, John D Kirwan2, Carsten Lüter3, Esther Ullrich-Lüter3
1Oxford University Museum of Natural History, University of Oxford, Parks Road, Oxford OX1 3PW,
UK.
2Stazione Zoologica Anton Dohrn, Via Francesco Caracciolo, 333, 80122 Naples, Italy.
3Museum für Naturkunde, Leibniz Institute for Evolution and Biodiversity, Invalidenstrasse 43, 10115
Berlin, Germany.
*Corresponding author: [email protected]
Key words: Echinoderms, extraocular vision, ophiuroids, vision
© 2021. Published by The Company of Biologists Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution and reproduction in any medium provided that the original work is properly attributed. Journal of Experimental Biology • Accepted manuscript Summary statement
Sumner-Rooney et al. characterise responses to static visual stimuli of varying size and contrast, as well as to moving shadows, in a brittle star.
Abstract
Spatial vision was recently reported in a brittle star, Ophiomastix wendtii, which lacks discrete eyes, but little is known about its visual ecology. Our aim was to better characterize the vision and visual ecology of this unusual visual system. We tested animals’ orientation relative to vertical bar stimuli at a range of angular widths and contrast, to identify limits of angular and contrast detection. We also presented dynamic shadow stimuli, either looming towards or passing overhead the animal, to test for potential defensive responses. Finally, we presented animals lacking a single arm with a vertical bar stimulus known to elicit a response in intact animals. We found that O. wendtii orients to large (≥50°), high-contrast vertical bar stimuli, consistent with a shelter-seeking role and with photoreceptor acceptance angles estimated from morphology. We calculate poor optical sensitivity for individual photoreceptors, and predict dramatic oversampling for photoreceptor arrays. We also report responses to dark stimuli moving against a bright background - this is the first report of responses to moving stimuli in brittle stars and suggests additional defensive uses for vision in echinoderms. Finally, we found that animals missing a single arm orient worse to static stimuli, which requires further investigation.
Journal of Experimental Biology • Accepted manuscript Introduction
Light is a critical biological cue, and detecting it can play a role in habitat selection, defensive behaviour, UV protection, and biological rhythms. Image-forming vision can facilitate more complex behaviours including navigation, communication and pursuit (Nilsson, 2013). Eyes – discrete sensory organs that facilitate vision – have evolved dozens of times among animals and exhibit a stunning diversity of forms (Land and Nilsson, 2012; von Salvini-Plawen and Mayr, 1977). Many animals also detect light using extraocular photoreceptors, in the brain, skin, in intrinsically light-sensitive neurons, or elsewhere (e.g. Battelle, 2016; Kingston and Cronin, 2016; Ramirez et al., 2011; Tong et al., 2009). Until recently, it was considered that these extraocular photoreceptors did not contribute to vision or visual processes (reviewed in Cronin and Johnsen, 2016).
Recent experiments evince extraocular photoreceptors mediating vision in echinoderms (Blevins and
Johnsen, 2004; Kirwan et al., 2018; Sumner-Rooney et al., 2020; Yerramilli and Johnsen, 2010). In both sea urchins (Ullrich-Lüter et al., 2011) and brittle stars (Delroisse et al., 2014; Johnsen, 1997;
Sumner-Rooney et al., 2018), putative photoreceptors are spread over the body surface, and in select species these appear to mediate responses to visual stimuli, undetectable by non-visual photoreception (Kirwan et al., 2018; Sumner-Rooney et al., 2020).
The occurrence of extraocular vision in at least two classes of echinoderms opens up a host of new questions and potential research avenues concerning their function, limitations, signal integration, and evolution. Our fundamental understanding of vision has been built on centuries of work on animal eyes. Distributed visual systems, including those of ark clams and fan worms (Nilsson, 1994), break from many of the conventions of paired eyes, but still retain discrete visual units. Extraocular systems, however, cannot be easily described optically because photoreceptors are not arranged in adjacent rows within a discrete structure, making properties such as acceptance angle more difficult to estimate. These animals therefore represent a challenge for visual biologists. With a better understanding of extraocular visual systems and their capabilities, we may also find new resources
Journal of Experimental Biology • Accepted manuscript and inspiration for biomimetic sensor technology (e.g. Aizenberg and Hendler, 2004; Mao et al.,
2013; Watanabe et al., 2011; Yang and Aizenberg, 2005).
The brittle star Ophiomastix wendtii (Müller and Troschel, 1842; formerly Ophiocoma wendtii, according to O’Hara et al., 2019) orients to isoreflectant stimuli. These reflect the same amount of light, in total, as the background against which they are presented, and are therefore detectable only via object resolving vision (Sumner-Rooney et al., 2020). Ophiomastix wendtii inhabits densely populated reef rubble in the Caribbean and Gulf of Mexico, where predation pressure is high.
Parrotfish, wrasse and mojarra are all reported to feed on members of the genus, with the greatest threat from Sparisoma and Halichoeres spp. (Hendler, 1984). These are large, fast-moving diurnal species that are present in high numbers and particularly parrotfish and mojarra may consume whole animals (Hendler, 1984). Orientation to these static stimuli may reflect motivation to seek shelter in bright, heterogenous reef rubble habitats, and that animals are attracted to regions of local contrast that might indicate structural heterogeneity and therefore potential refuge from predation (Sides and Woodley, 1985).
Clarifying the visual acuity exhibited by Ophiomastix would shed light on both visual function and visual ecology in relation to this behaviour; for example, Sides and Woodley (1985) suggested that O. wendtii maintained sympatry with other ophiocomids by selecting larger crevices in which to shelter.
This could reflect a limit on acuity or a selective preference. Moreover, high contrast signals (as used by Sumner-Rooney et al., 2020) are uncommon in oceanic water, and investigating contrast sensitivity at detectable spatial frequencies (once identified) helps infer how performance and visual ecology interrelate. Although the habitat of O. wendtii is shallow and bright, we might expect animals to respond to lower contrast signals more representative of natural scenes if this behaviour is biologically relevant.
Journal of Experimental Biology • Accepted manuscript Other uses for low-resolution vision may exist, besides habitat selection. To date, only static stimuli have been tested in Ophiomastix, but their natural visual environment is busy and dynamic.
Responses to moving stimuli might reveal additional or alternative roles of vision in predator detection. In Diadema, both the sudden and looming appearance of dark stimuli against a bright background elicited a characteristic defensive spine-pointing response. In other distributed visual systems, including chiton shell eyes, ark clam compound eyes and fanworm radiolar eyes, predator detection is the core task of vision (Bok et al., 2019; Nilsson, 1994; Speiser et al., 2011). Other than arm autotomy, defensive or harm-reductive behaviours are not extensively documented in brittle stars. Hendler (1984) reported that arm spines would raise and lock into place and that animals produce mucus when they are mechanically disturbed. The nocturnal activity patterns and proposed shelter-seeking of O. wendtii may contribute to their avoidance of predation, but given their vulnerability to fast-moving visual predators during the day, we might expect them to respond to moving shadows.
How animals might integrate information from thousands of dispersed photoreceptors remains uncertain. Sumner-Rooney et al. (2020) highlighted a distinction in locomotion between sighted
Ophiomastix and a closely related but apparently non-sighted species Ophiocomella pumila (Lütken,
1856), which they proposed was a possible clue to signal integration. Leading with a single arm
(“rowing”; Astley, 2012) appears to be the dominant locomotory mode in most ophiuroid species studied to date (Arshavskii et al., 1976; Astley, 2012; Clark et al., 2018; Glaser, 1907; Wakita et al.,
2020). “Reverse rowing” (Astley, 2012), with two leading arms, is also widely reported but seems to be less common. While O. pumila almost always moved by rowing, O. wendtii used reverse rowing in the majority of experiments (Sumner-Rooney et al., 2020). These authors suggested that leading with two outstretched arms could indicate signal comparison between them in O. wendtii; the complex and variable body shape and relatively rapid movement of Ophiomastix likely presents significant additional challenges for extraocular vision in comparison to the fixed spherical shape of sea urchins. Comparing pooled photoreceptor signal between adjacent arms could be a much
Journal of Experimental Biology • Accepted manuscript simpler method of contrast detection than integrating spatial signal within arms or across the whole body. Previous authors have suggested that each arm acts as a semi-autonomous system (reviewed in Yoshida, 1966), and Stubbs (1983; unpublished thesis) demonstrated that electrical responses to the illumination of one arm can be detected in the radial nerve cord of another. If communication between adjacent arms were used during stimulus detection and approach, arm damage or loss could impede this ability. Although brittle stars readily autotomise arm portions or entire arms during defensive behaviours, previous experiments have been restricted to intact animals. We therefore repeated one of the experiments of Sumner-Rooney et al. (2020) using animals missing a single arm to study the effects of arm loss on orientation responses.
We aim to better characterise the visual performance of Ophiomastix, identifying fundamental thresholds to visual behaviour and testing responses to established dynamic stimuli. In determining these thresholds, we hope to gain a better understanding of the visual ecology, and ultimately, the evolution of this unusual visual system.
Materials and methods
Specimens
Adult Ophiomastix wendtii were collected in May-June 2017 and June-July 2019 at Punta Hospital,
Isla Solarte, Panama (9°19’44.4’’N, 82°12021.6’’W, 0–3 m), and housed in open-air aquaria at the
Smithsonian Tropical Research Institute in Bocas del Toro, Panama (MiAMBIENTE research permits
SE/A-35-17 and SE/A-48-19). Animals were given three days to recover from collection before experiments. Those that autotomised arms were excluded from experiments unless otherwise stated. Animals were exposed to each stimulus only once and were tested up to twice per day.
Animals collected in 2017 measured a mean of 105.8 mm (SD=21.6 mm) from the centre of the disc to the tip of the longest arm. Animals collected in 2019 measured 107.4 mm (SD=17.3 mm). Sex of the animals was unknown.
Journal of Experimental Biology • Accepted manuscript Orientation experiments
Animals were placed at the centre of a circular arena (60 cm Ø, depth 50 cm) filled with unfiltered seawater, and with a stimulus pattern presented on the inside wall on printed vinyl (Figure 1A).
Animals move linearly from the centre to the edge of the arena (Sumner-Rooney et al. 2020). We measured angular bearings of animal position (both absolute and relative to the centre of the stimulus) when the disk first touched the arena wall. The position of the stimulus was changed between every trial, being randomly selected each time from a list of eight positions at 45° increments (i.e. 0°, 45°, 90°, etc.) The arena floor and walls were cleaned, and seawater was replenished, between trials. Experiments were performed in natural daylight beneath a diffuser comprising multiple layers of white cotton. Solar irradiance is monitored by the STRI physical monitoring programme using a Kipp & Zonen SP-Lite2 pyranometer (sensitivity 400-1100 nm), with mean irradiance being measured every 15 minutes. Experiments were conducted between 10am and 3:15pm to avoid spectral impacts of sunrise (6:10-6:15am) and sunset (6:45-6:50pm). To ensure that the stimuli reflected proportionately, the reflectance of a series of test pieces (of printed vinyl with relevant grey values) was measured using an RPS900-R spectroradiometer (International Light,
MA, USA) in air. The spectroradiometer recorded the relative counts of light reflected by each of the test pieces and by a highly reflective white standard. Counts were measured across the visible range of wavelengths (300 to 700 nm, at 0.45 nm intervals). All stimulus contrasts are Michelson’s contrasts, given by:
Eqn 1.
Where Fmax and Fmin are the maximum and minimum values of the stimulus (darker and lighter vertical bars).
Journal of Experimental Biology • Accepted manuscript Stimulus size
To find the resolution to which animals respond, subjects were presented with discrete bar stimuli: a central black target with white flanks half as wide, with a total angular width from 20° to 70° (in 10° increments) of the arena walls, which were elsewhere an intermediate grey. The reflectance of black and white areas within each stimulus counterbalanced one another, making stimuli isoreflectant to the background, as confirmed by reflectance measurements (Figure 1B,C). These black and white stimuli had Michelson contrast of 0.95 (due to reflectance in the dark region). Experiments using a stimulus of 50° width were performed in May-June 2017; all other experiments were performed using an identical set-up, animals of similar size (see Specimens), and following identical procedures in June-July 2019.
Contrast sensitivity
To assay whether O. wendtii detects low contrasts, two variants of the 60° centred vertical bar stimulus were added: These differed from the main stimulus in having proportionately reduced amplitude light and dark bars, with the Michelson contrast between the light and dark parts reduced from 0.95 to 0.1 and 0.05, respectively. The total stimuli (light and dark bars combined) were isoreflectant with the background of the arena (Figure 1B,C).
Arm loss
We tested 29 animals that autotomised a single arm (to below a quarter of adjacent arm length), as above, for orientation to a 60° stimulus of Michelson contrast 0.95. Animals were placed in the centre of the arena with the missing arm randomly oriented in relation to the stimulus centre. Initial body orientation, terminal body orientation, and terminal bearing were recorded.
Journal of Experimental Biology • Accepted manuscript Analysis
To analyse orientation data (bearings at the end of a trial), we used two approaches, either treating the data as circular, and distributed according to a von Mises distribution, or discretized: partitioned into success if they fell within a 60° sector centred on the stimulus midpoint, or failure otherwise.
The orientedness of the absolute (to true north) bearings combined across all treatments was compared to a range of orientation models using maximum likelihood estimates to test for a general directional bias using the Circ_MLE package in R (Fitak and Johnsen, 2017). All further analyses used bearings relative to the stimulus midpoint.
We assessed the likelihood of models representing differing distributions of circular data (hereafter, circular MLE) using the Circ_MLE package (Fitak and Johnsen, 2017) with the AICc criterion for small sample sizes. Circular data were also modelled using Bayesian probability and compared to controls
(see supplementary data).
We modelled the psychometric function (Houpt and Bittner, 2018; Kirwan and Nilsson, 2019) using
Stan (Carpenter et al., 2017) via the R package brms (Bürkner, 2017). We used informative priors to regularize and we inspected their influence graphically (Figure SF1). We further modelled stimulus detection at three levels of Michelson contrast (0.95, 0.1 and 0.05) treated categorically. In both cases, the model was run for 5000 sampled iterations across 4 chains and tested by visually inspecting chain traces, inspecting Rhat and effective sample size values, and a graphical posterior predictive check (supplementary figure S1).
The time taken to complete the experiment (measured from settling at the centre of the arena to the disc making contact with the wall) was recorded and compared between control, and 20°-70° stimuli using Kruskal-Wallis, followed by Mann-Whitney U tests for multiple pairwise comparison of levels.
Journal of Experimental Biology • Accepted manuscript To confirm that terminal bearings were an accurate representation of animals’ orientation behaviour, available videos of experiments using 20°, 70° and control stimuli (n=89) were reviewed and the animals’ path tracked in full using the DORIS object tracking software
(https://github.com/olivierfriard/DORIS). Animals were tracked using a coordinate system with the origin at the centre of the arena, and scaled to real size using the arena diameter. The black centre of the stimulus (in the 20° and 70° experiments) was tracked to record its relative position to the animal. Coordinates were converted to trajectories and analysed using the Trajr package (McLean and Skowron Volponi, 2018) in R (R Development Core Team, 2014). To compare initial direction of movement to terminal direction, a circle of 10 cm diameter was superimposed onto animal tracks, centred on the animals’ starting position. Their initial heading was measured at the point the animal crossed the perimeter of this circle, and this was subtracted from their terminal bearing to evaluate change of direction during the trial. To assess tortuosity, trajectories were rediscretised to a constant step length: mean step length across all trajectories was 0.0038 ± 0.0007; in order to capture all observed steps but lose minimal detail, a step size of 0.1 was chosen by visual comparison of step sizes 0.1, 1, 2 and 10. Characterising the trajectories as directed paths, the straightness of each trajectory was assessed using r, the length of the mean vector of turning angles
(Batschelet, 1981). In case the animals’ movement was better represented as a random walk
(though this did not appear to be the case from plotted trajectories), we also calculated sinuosity, a function of the mean cosine of turning angles (Benhamou, 2004). Straightness indices were compared between treatments using Kruskal-Wallis, followed by Mann-Whitney U tests for multiple pairwise comparison of levels, due to non-homogeneity of variances. Sinuosity was compared between treatments (control, 20° and 70° stimuli) using ANOVA, followed by Tukey’s test for multiple pairwise comparison of levels.
Journal of Experimental Biology • Accepted manuscript Loom and overhead pass stimuli
Fourteen animals were individually placed in a small tank (15 x 25 x 15 cm, Figure 2) covered on three sides with white paper backed by lightproof matte black plastic. A WLED-backlit display was positioned directly above the tank to present stimuli. We waited four minutes for the animal to habituate below a plain white screen, whereupon we presented a looming stimulus (black circle of initial diameter 13 mm/10° and final diameter 93 mm/70°, approaching over 0.5s). In other taxa, loom responses are rapid and often mediated by dedicated neurons or reflex responses (De
Franceschi et al., 2016; Oliva et al., 2007; Schlotterer, 1977; Yamawaki and Toh, 2009; Yilmaz and
Meister, 2013). Cobb and Hendler (1990) recorded spiking in the radial nerve cord in response to overhead illumination and shading less than 0.1s after stimulation in O. wendtii, indicating that temporal frequency is higher than is reported in sea stars (Garm and Nilsson, 2014). The main predators of O. wendtii are Halichoeres spp. and Sparisoma spp. (Labridae and Scaridae; Hendler,
1984). Mean observed speeds of labrids in the field range from 20-55 cm s-1 (Fulton et al., 2005;
Wainwright et al., 2002), with burst and attacking speeds likely to be substantially faster (e.g. see
Walker and Westneat, 2002), and parrotfish can clock up to more than 90 cm s-1 (Korsmeyer et al.,
2002). A loom over 0.5 s was thus chosen to reflect ecologically relevant speeds while spanning roughly ten times the reported temporal frequency. We then waited a further four minutes before presenting a circle of constant size moving horizontally across the screen (diameter 93 mm, moving at 6 cm s-1). The speed of the overhead pass stimulus reflected an angular speed of 33.4° s-1 as viewed from the bottom of the tank, corresponding to Halichoeres passing at a distance of 30-60 cm from the viewer (20-40 cm s-1, Wainwright et al., 2002) or Sparimosa at a distance of 60-120 cm (40-
80 cm s-1, Korsmeyer et al., 2002). Both stimuli occupied a maximum angular width of 70° as viewed from the bottom of the tank, which is larger than dark static stimuli demonstrated to provoke orientation responses (50°, Sumner-Rooney et al., 2020).
Journal of Experimental Biology • Accepted manuscript Analysis
Animal responses were scored blind by five independent observers, using videos of the experiments with the stimulus cropped out. Observers were shown a collection of training videos demonstrating responses and non-responses, before scoring the presence of responses from 36 videos. Of these, 14 contained an overhead pass, 14 contained a loom, and 8 lacked stimuli (i.e. blank white screen) as a negative control. Timings of responses were not reported by observers, only presence/absence. The presence or absence of a recorded response was modelled using Stan (Carpenter et al., 2017) via the
R package brms (Bürkner, 2017), with stimulus type as a fixed effect and animal identity and observer identity as random factors. The model was run for 4000 sampled iterations across 4 chains.
Modelled data for loom and overhead pass stimuli were then contrasted against control data to assess the probability that animals responded to stimuli. The proportion of the response distributions greater than the control (zero) can be interpreted as the probability that the corresponding stimulus elicited a response.
Results
Orientation experiments
Analysis of absolute bearings, prior to correction for the stimulus position, returned ΔAICc=0 for the uniform M1 distribution. No other distributions were supported with ΔAICc<2. All subsequent results are reported as bearings relative to the centre of the stimulus. Mean solar irradiance during orientation experiments examining stimulus size was 379.25 W m-2 (SD=291.25 W m-2). During experiments examining stimulus contrast, mean irradiance was 443.6 W m-2 (SD=267.8 W m-2). For a summary of irradiances for each stimulus, see supplementary data Table S1.
Journal of Experimental Biology • Accepted manuscript Stimulus size
Animals oriented towards stimuli that occupied 50° of the arena wall and above, according to maximum likelihood comparisons (Figure 3A, Table 1). Maximum likelihood comparisons returned the strongest support (AICc=0) for axial bimodal (50° stimulus) and unimodal (60° and 70° stimuli) distributions, with all circular means within 10° of the centre of the stimulus (Table 1). Animals presented with stimuli of 20-40° angular width were found to be disoriented relative to stimulus position (Figure 3A, Table 1; AICc=0 for M1 uniform distribution).
Psychometric models of success/failure to locate the stimulus were uncertain regarding a threshold point for successful orientation (Figure 3B), but a 50% confidence interval for the threshold was estimated at 41-63°.
We did not observe pronounced orientation towards the internal edges of the stimulus patterns, the area of the highest local contrast, despite potential indications of this in Sumner-Rooney et al. (2020:
Figure 1). We interpreted bearings as absolute deviations from 0°, i.e. from 0-180°, to examine this possibility, but animals did not exhibit a particular attraction to the internal stimulus edge (mean bearings 64°-96.5°; Supplementary figure S2).
Stimulus size (control, 20°-70°) also explained a significant part of the variation in time taken to complete the experiment (Kruskal-Wallis, χ2=32.219, p<0.0001; Figure 4A). Post hoc pairwise comparisons indicated that animals presented with control stimuli took significantly longer to complete the experiment than those presented with 30°-70° stimuli (Pairwise Mann-Whitney U test,
Bonferroni correction for multiple comparisons, padj<0.01), and that animals presented with the 20° stimulus were slower than those presented with the 60° stimulus (padj=0.03).
Plotted trajectories for animals presented with control, 20° and 70° stimuli demonstrated that terminal bearing reliably represents the direction of travel (Figure 4B). Trajectories appear to represent directed paths, and straightness indices were very high for all stimuli (0.96-0.976, Figure
Journal of Experimental Biology • Accepted manuscript 4C, Table 2). Comparisons of initial headings and terminal bearings demonstrated that animals rarely changed direction during the experiment; differences between these clustered around 0°
(Supplementary figure S3). Mean change in direction ranged from 358° (control, rho=0.85) to 3° (70° stimulus, rho=0.97), and maximum likelihood comparisons for all three stimuli returned strongest support for unimodal distributions around these.
While straightness was high for tracked animals presented with control, 20°, and 70° stimuli, we found that it varied between them (Kruskal-Wallis, χ2=11.237, p=0.0036), with post hoc analysis indicating that animals presented with visual stimuli took straighter paths than those presented with the control (Pairwise Mann-Whitney U test, Bonferroni correction for multiple comparisons, control vs. 20° padj=0.036, control vs. 70° padj=0.0062, Figure 4C). Sinuosity also varied significantly according to stimulus size (ANOVA, F=9.418, p=0.0029), being significantly higher in animals presented with the control than the 70° stimulus (Tukey’s multiple comparisons, padj=0.00375, Figure 4D).
Contrast sensitivity
Animals presented with 60° stimuli with Michelson’s contrasts of 0.1 or 0.05 were found to be disoriented by maximum likelihood analyses (Figure 5A; Table 1). Animals were found to orient to a
60° stimulus with Michelson’s contrast of 0.95 as described above.
A categorical model of contrast treatments using Bayesian inference supported a response only to a
Michelson contrast of 0.95 (Figure 5B).
Arm loss
The direction of animals’ movement during these experiments appears to have been affected by the orientation of the missing arm. The direction of animal movement from their initial to their terminal position in the arena, relative to the position of the missing arm, was non-uniformly distributed; animals appeared to move with the missing arm trailing (Figure 6A, Table 3; µ=178°; ∆AICc=0 for
M2B, unimodal clustering, ϕ=191°, ∆AICc<2 for M2A, unimodal clustering, ϕ=178°).
Journal of Experimental Biology • Accepted manuscript Despite orientation to the same stimulus in intact animals, terminal bearings relative to the position of the stimulus were disoriented for animals missing one arm (Figure 6B; Table 3; ∆AICc=0 for M1, uniform distribution, no other model returned ∆AICc<2). Five of these animals began the experiment with the armless side directed towards the stimulus (i.e. the offset between the two midpoints is below 36°). Given that the position of the missing arm appears to directly affect terminal bearing in an axial fashion, these animals might be expected to move away from the stimulus artifactually (four of them did so). When these five animals were excluded from analyses of orientation, terminal bearings of the remaining animals clustered around the position of the stimulus (Figure 6C, Table 3;
µ=341°). Maximum likelihood analyses returned strongest support for a unimodal distribution centred on the stimulus (M2C, ϕ=349°, Table 3), as well as additional support (∆AICc<2) for two other unimodal distributions (ϕ=341°) and the M1 uniform distribution.
Animals did not substantially change their body orientation during experiments. Animals lead with the same arm or arms throughout the experiment in all cases, and the difference between initial and terminal orientation of the missing arm clustered around 0° (Figure 6D, Table 3; ∆AICc=0 for M2A, unimodal clustering, ϕ =356°, no other model returned ∆AICc<2). This accords with previous work demonstrating that brittle stars seldom change direction by rotating the central disk (Astley, 2012).
Loom and overhead pass stimuli
Responses to dynamic stimuli were generally subtle, constituting sudden jerks of the arms or raising of the dorsalmost spines. Overall, a response was recorded for 67% of looms, 50% of overhead passes, and 35% of controls. The model found that animals respond to both loom and overhead pass stimuli but not to a negative control (Figure 2).
Journal of Experimental Biology • Accepted manuscript Discussion
Overall, our results lend further support to predator evasion being the primary role of the visual system in Ophiomastix wendtii. Animals orient towards large, high-contrast vertical bar stimuli and exhibit potentially defensive responses to overhead shadows. Orientation is preserved in animals that have undergone natural autotomy of an arm, provided that the missing arm is not directly facing the stimulus. Arm loss is very common in ophiuroids, and Sides (1987) reported that 29.5% of collected O. wendtii were regenerating at least one arm, so the persistence of orientation behaviour despite an amputation will be relevant to a decent proportion of individuals.
Behavioural thresholds
A distinction between behavioural responses to 40° and 50° stimuli emerges from our data, potentially reflecting an important threshold in the visual ecology of O. wendtii. Maximum likelihood analyses indicate a behavioural threshold between 40°-50° angular width, within the range identified by the psychometric function, and Bayesian probability estimates indicated that animals were very likely oriented to 50° and 60° stimuli (see Supplementary Data, Table S1, Supplementary figure S4).
Although animals presented with 50°, 60° and 70° stimuli returned the greatest support for different orientation models, we consider them all to indicate orientation towards the stimulus. The axial bimodal (M4B) distribution, recovered for the 50° stimulus, describes animals moving in two axially opposed directions (ϕ1, ϕ2; here, directly towards and away from the centre of the stimulus; see
Table 1). However, the concentration of animals around these two directions (κ1, κ2) and their distribution between them (λ) is unequal. In this case, concentration around the stimulus was more than two orders of magnitude greater than concentration away from the stimulus (Table 1), and 73% of animals were considered by the model to be oriented towards the stimulus (λ=0.73; see Schnute and Groot, 1992). The two unimodal distributions (M2A and M2B) differ in that λ=1 for M2A; i.e. all animals are considered to be oriented in the modal direction. This is not the case in M2B (or M2C, recovered for animals missing an arm), wherein a random variable causes departure from λ=1
Journal of Experimental Biology • Accepted manuscript (Schnute and Groot, 1992). Although estimation of resolution via the psychometric function was uncertain, this analysis considers a threshold of 41-63° most probable (50% CI). This method is preferred as it incorporates relevant prior knowledge, uses responses discretised based on orientation to the target, which is more directly relevant than angular headings, and illustrates the uncertainty of the estimate.
There are several possible explanations for the observed behavioural threshold between 40° and 50° stimuli. First, this could reflect a limit of angular detection, i.e. directly related to the resolution of the visual system. Several morphological characteristics of a visual system can affect its performance; however, the distributed nature of the system in Ophiomastix means functional interpretations based on our understanding of discrete lensed or compound eyes should be treated cautiously.
When compared to a sine grating with a period of the stimulus angular width, the centred vertical bar stimulus is isoluminant but slightly more conspicuous (greater remaining contrast) when viewed through an equivalent system with equal resolution (Supplementary Figure S5). Resolving a grating with a period of 50° requires a photoreceptor acceptance angle (Δ⍴) of 25° or smaller (Land, 1997;
Land and Nilsson, 2012). The acceptance angle of light-adapted photoreceptors in O. wendtii was estimated to be 31° based on morphological models (Sumner-Rooney et al., 2020), a reasonable match to orientation behaviour. To estimate acceptance angles, Sumner-Rooney et al. measured aperture widths from reconstructed models of photoreceptors situated within the skeleton and surrounded by pigment granules. Photoreceptors are located within skeletal pores and bear a distal projection that expands at the tip. Apertures were measured from the base of these expansions, which are strongly reactive to antibodies raised against sea urchin r-opsin and are presumed to be the primary sensory surface. From angular apertures, photoreceptor acceptance angles were approximated on the assumption that the angular sensitivity function is Gaussian and that 99% of
Journal of Experimental Biology • Accepted manuscript detected light enters through the aperture. Nilsson (2013) calculated the maximum detection angle that could reliably support low-resolution vision as 40°.
The composition of the photoreceptor array also contributes to the performance of the system by determining the sampling resolution. In many contiguous retinas, the inter-receptor and receptor acceptance angles are closely related, but the photoreceptors in O. wendtii are dispersed across the body surface and located in skeletal pores 30-40 µm apart. Despite this large translational separation, their angular separation appears to be relatively small, owing to the shallow gradient of the arm plates and the number of receptors: the mean angular separation of adjacent pores (each containing a single photoreceptor), measured from synchrotron scans of O. wendtii (see Sumner-
Rooney et al., 2018), was 6.7° (S.D. 2.1°; n=31) on the dorsal arm plates. This gives Δ⍴/Δɸ=4.67, reflecting dramatic oversampling (where Δ⍴/Δɸ>2, Land, 1997). The space sampled by adjacent photoreceptors in O. wendtii therefore overlaps considerably: in an idealised regular hexagonal array, this would result in any part of the visual scene being sampled by 12-13 photoreceptors, potentially contributing to increased sensitivity. However, we don’t know whether information from the many thousands of cells is combined to form one or more images; it may be that the distribution of photoreceptors in O. wendtii does not represent the organisation of a retina and thus we should make such comparisons cautiously.
Although information on signal integration between adjacent photoreceptors is lacking, previous immunohistochemical studies found that afferent axons from groups of adjacent photoreceptors coalesced into bundles within the stereom. This could indicate summation or similar, but this remains purely speculative (Sumner-Rooney et al., 2018; Sumner-Rooney et al., 2020). Additionally, though individual dorsal arm plates are a relatively simple surface, these photoreceptors are found on the lateral and ventral plates, almost the full length of the arms (Sumner-Rooney et al., 2018;
Sumner-Rooney et al., 2020). This would result in a highly irregularly shaped field of view, and one that would change dramatically and rapidly as the animal moved.
Journal of Experimental Biology • Accepted manuscript The behavioural threshold identified at 40°-50° may instead underestimate resolving power but reflect ecological relevance. Animals may be uninterested in smaller stimuli if, for example, they represent objects too distant or too small to act as effective shelters. Indeed, Sides and Woodley
(1985) suggested that selection of larger shelters could contribute to niche separation between sympatric ophiocomid species. Although the occupation of a crevice is likely to be based on body size, this could confer an advantage to selectively orienting to large objects. Animals completed experiments significantly faster when presented with a high-contrast stimulus of any angular width than when presented with a control, potentially indicating that stimuli of 20°-40° are detectable, but perhaps do not indicate a suitable shelter. We did not observe significant orientation away from these, so it’s more likely that they are uninteresting than repellent, but their presence could have another impact, such as initiating movement or helping to maintain a straight path. Although the straightness of animal paths in response to a 20° stimulus was found to statistically differ from neither a control (padj=0.1) nor a 70° stimulus (padj=0.77), there is a consistent upward trend between straightness and stimulus size (Figure 4C) that could further support this hypothesis.
Given the strong photonegative behaviour of O. wendtii, we expected to find evidence for high contrast sensitivity. However, none of our analyses supported orientation to stimuli of Michelson contrast 0.1 or 0.05. The Land optical sensitivity equation, solved for an individual photoreceptor, gives a predicted sensitivity of 0.175 in O. wendtii (for broad-spectrum light given the shallow habitat, equation 1) (Kirschfeld, 1974; Land, 1981; Warrant and Nilsson, 1998). Here, D, ρ, and l are receptor diameter (5 µm, Sumner-Rooney et al. 2018), acceptance angle (31°, 0.54 radians, Sumner-
Rooney et al., 2020) and length (15 µm, length of observed distal expansions in Sumner-Rooney et al., 2018), respectively, and k is a typical absorption coefficient for a rhabdomeric photoreceptor
(0.0067 µm-1; Warrant and Nilsson, 1998).
( ) ( ) Eqn 2.
Journal of Experimental Biology • Accepted manuscript The resulting value is low, being broadly comparable to the marine worm Vanadis or the honeybee
Apis mellifera (Cronin et al., 2014; Land, 1981); however, these systems both have much smaller acceptance angles of <2°. The very low calculated optical sensitivity predicted in Ophiomastix results from the dispersed nature of the system: a combination of a very small aperture (for each individual photoreceptor, rather than the pupil of an eye) and lack of focussing optics, despite the large acceptance angle. Thus, although the visual scene in the experimental arena was bright, poor optical sensitivity could somewhat limit the detection of the very low-contrast stimuli used in our experiments. The reef habitats of O. wendtii are shallow, bright and structurally complex, so even poor contrast sensitivity may be sufficient to detect large objects during the day, when putative shelter-seeking would be most important. However, given that the range of untested stimulus contrasts, from 0.1 to 0.95, encompasses a very wide range of natural values, future attempts to identify contrast thresholds should use intermediate levels.
Arm loss and integration
The possibility that animals integrate photoreceptor signals across the body in a way at all analogous to facets of a compound eye seems remote; the irregularity and flexibility of the body surface would surely be a computational nightmare. Sumner-Rooney et al. (2020) noted that O. wendtii frequently moved by reverse rowing, with two outstretched arms leading the animal (Astley, 2012) and suggested that this indicates signal integration between adjacent arms that facilitated detection or orientation. Although we cannot conclude whether signals are compared between whole arms, we find that the removal of a single arm affects preferred direction of travel and impairs motivation and/or orientation to stimuli. The rate of reverse rowing in these experiments was around 50%, in line with previous observations of intact animals (but higher than previously observed in Ophiocoma echinata; Astley, 2012; Sumner-Rooney et al., 2020).
Journal of Experimental Biology • Accepted manuscript We attempted to test whether orientation ability is affected in animals that had lost an arm, but the loss itself appears to impact preferential direction of travel, with a notable trend of animals trailing the missing arm (Figure 5A). This contradicts findings by Yoshida and Mori (Yoshida 1966) that the positively phototactic sea urchin, Temnopleurus toreumaticus, preferentially moves towards its operated side when a single radial nerve is cut, in the absence of a photostimulus. Asterias amurensis was also found to move towards arms with ocelli removed, or towards the direction of a single amputated arm (Yoshida and Ohtsuki, 1968). They suggested that this supported an inhibitory role of the ocellus, which was removed with amputation. In contrast, Clark et al. (2018) reported three modes of movement in Ophiarachna incrassata when one arm is isolated by cuts to the central nerve ring, two of which involved the isolated arm trailing (Clark et al., 2018: Figure 6), aligning with our findings. This may reflect the rather different biomechanics of ophiuroids, which use the articulated arms rather than the tube feet for locomotion and thus may be more physically impaired by such operations. It’s also worth noting that both Temnopleurus and Asterias are positively phototactic and move towards the operated side, whereas both O. wendtii and O. incrassata are photonegative and move away from it; in both cases, the absence of signal may replicate an ‘on’ response.
Animals that were placed in the arena with the missing arm facing the stimulus did not orient to it; however, whether this is the direct result of biomechanical damage influencing direction or an inability to detect the stimulus is unclear. When an intact arm was oriented to the stimulus at the beginning of a trial, animals were able to locate it, indicating that detection does still play a role in the context of damage, and the biomechanical effects of arm loss do not completely override this behaviour. Similarly, Yoshida and Kobayashi (Yoshida, 1966) found that T. toreumaticus never moved directly towards a light source on their operated side, but they did observe animals rotate and then lead with an intact side. Drawing conclusions about integration from these data would be premature, but it is notable that even where a missing arm faces the centre of a stimulus of 60° angular width, the stimulus is likely to be partially within the field of view of the two adjacent, intact
Journal of Experimental Biology • Accepted manuscript arms. If so, detection by single or non-adjacent arms would not appear to be sufficient to affect orientation. The nerve ring is intact, so communication between the remaining arms (as observed by
Stubbs, 1983; unpublished thesis) should be unimpeded.
To clarify whether two adjacent arms are required for stimulus detection, future experiments could use animals with two arms removed, either side of a single intact arm, and place animals in the arena with this intact arm facing the stimulus. If one arm is sufficient for detection, animals might be expected to orient towards the stimulus, but if communication between adjacent arms is required, we would expect disorientation. If the removal of two arms has a greater impact on direction of travel than the presence of the stimulus, animals may orient directly away from the stimulus, assuming that the animal will move away from removed arms as observed in the current study (and in line with similar experiments in Asterias by Yoshida and Ohtsuki, 1968). If the latter is not the case, then orienting animals with the pair of intact, adjacent arms facing the stimulus may recover orientation behaviour. This potentially has important ramifications for animal survival; in predation experiments, Hendler (1984) exposed twelve specimens of O. wendtii on open reef floor, alongside individuals of three other species, and reported 27 attacks on four of them in the space of three minutes.
Dynamic stimuli
Our model indicates that animals were highly likely to respond to both loom and overhead pass stimuli, compared to control experiments. Looms are ecologically relevant as they may represent an approaching threat, and loom responses are widespread in other taxa (e.g. Oliva et al., 2007;
Yamawaki and Toh, 2009; Yilmaz and Meister, 2013). Uniform shading or shadows passing overhead can produce mixed or different responses in other taxa, such as freezing, likely signifying a reduced level of immediate threat (De Franceschi et al., 2016). However, distinguishing between these threats require more sophisticated processing than we find in O. wendtii. We tried to approximate
Journal of Experimental Biology • Accepted manuscript ecologically and physiologically relevant speeds and sizes in our experiments, based on existing knowledge of both O. wendtiii and its predators, that might be most likely to evoke responses.
However, we cannot conclude that Ophiomastix responds specifically to dynamic stimuli, as they may have responded to the appearance of a dark object overhead. Response time, which could indicate a critical angular size of approaching object, was not recorded. Nonetheless, responsiveness to the appearance of a dark stimulus demonstrates a second function of the visual system in O. wendtii in addition to shelter-seeking. This may reflect the high predation pressure in the crowded reef rubble habitats of O. wendtii, with fish readily attacking exposed animals (Hendler, 1984; LSR, pers. obs.). Responses to dynamic or appearing stimuli do not require spatial resolution, and ‘alarm’ photoreception has been described as a distinct class of visual task by Nilsson (2013). All examples of alarm photoreception therein (e.g. ark clams and sabellid worms) are taxa with distributed visual systems, where individual units may not provide image information (Nilsson, 1994; Nilsson, 2013).
The detection of shadows by O. wendtii fits well into this category, suggesting that this response may not be reliant on image formation. In addition, Nilsson (1994) found that both ark clams and sabellids extensively oversampled the visual field, with dozens or even hundreds of ommatidia overlapping. The sampling predicted in O. wendtii is less dense than these examples, but may still benefit from filtering out false alarms, reduced vulnerability to injury or biofouling, and increasing signal-to-noise ratio by pooling photoreceptor signals.
Conclusions
Ophiomastix wendtii is able to detect and respond to high-contrast static and appearing stimuli, indicating uses for photoreception and vision in both habitat selection and defensive behaviours. A behavioural threshold in orientation responses to stimuli of 50° width and above could be indicative of either a limit of detection or motivation. Anatomical evidence indicates that photoreceptor acceptance angles would be a good match for the required resolution. We observed the extinction of orientation to 60° stimuli at Michelson contrasts of 0.1 and below, and calculated poor predicted
Journal of Experimental Biology • Accepted manuscript optical sensitivity from morphology. We also report a response to moving stimuli for the first time in brittle stars, although its specificity cannot be confirmed at this stage. However, this indicates a defensive role for vision in addition to shelter-seeking. How signals are integrated between photoreceptors, arm segments or entire arms remains a considerable challenge. Future experiments could help clarify whether signal comparison between adjacent arms could play a role in detecting and locating visual stimuli.
Journal of Experimental Biology • Accepted manuscript Acknowledgements
We thank Arcadio Castillo, Cynthia Peña and Bailey Fallon for their assistance collecting animals,
Rachel Collin and Plinio Gondola for their continued support at STRI, James Foster for invaluable discussions of the analysis and providing R scripts, Yakir Gagnon for assistance with analysis, and
Julia Calderwood, Frankie Dunn, Duncan Murdock, Jin-Ho Park, and Imran Rahman for blind-scoring loom and overhead pass experiments. Solar irradiance data are provided by the Physical Monitoring
Program of the Smithsonian Tropical Research Institute. Three anonymous reviewers provided helpful comments that improved this manuscript.
Competing interests
The authors declare that they have no competing interests.
Funding
This work was supported by the Oxford University Museum of Natural History (fellowship to LSR),
DFG (UL 428/2-1, EUL), and the Human Frontier Science Program (RGP0002/2019, CL and JDK).
Author contributions
LSR, JDK and EUL conceived the study. LSR and JDK designed the behavioural experiments. LSR collected animals and ran behavioural experiments. LSR and JDK analysed results. CL supervised and managed the project. LSR wrote the manuscript with input from JDK and EUL and all authors edited and approved the manuscript.
Data availability
Data and R markdowns for all analyses will be made available on Github (github.com/XXXXXXXX) upon publication.
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Journal of Experimental Biology • Accepted manuscript Figures
Figure 1. Orientation experiments in Ophiomastix wendtii. A. Animals were placed at the centre of a circular arena with a vertical bar stimulus presented at one side and their movements were filmed from above. B. Stimuli varied in angular width (i,ii) or in Michelson contrast (iii,iv). C. Intensity profiles of the four example stimuli i-iv, demonstrating variation in width and amplitude.
Journal of Experimental Biology • Accepted manuscript
Figure 2. Ophiomastix wendtii reacts to shadows looming and passing overhead. Animals were placed within a small tank with an overhead screen that presented a loom stimulus (a growing black circle) or an overhead pass stimulus (a circle of the same maximum width passing across the screen).
Observers were blind to the presence or absence of stimuli, and reported presence or absence of a response from filmed experiments. Curves represent modelled responses to loom and overhead pass stimuli, accounting for animal and observer identity. The vertical line at log(kappa)=0 represents responses to a control stimulus. The proportion of the area under each curve that exceeds the control can be interpreted as the probability that animals responded to the stimulus.
Journal of Experimental Biology • Accepted manuscript
Figure 3. Ophiomastix wendtii responds to vertical bar stimuli of angular width 50° and above. The total angular width of the stimulus was increased from 20° to 70°, in 10° increments. Michelson contrast was 0.95. A. Terminal bearings were disoriented relative to stimuli of 20-40° angular width, but clustered around the centre of the stimuli 50° and above. Pink dots represent one individual, presented with the stimulus once. Arrows indicate the direction and length of the mean vector; blue brackets indicate maximum likelihood-based confidence intervals. B. Marginal effects at the mean of orientation towards the stimulus with respect to stimulus angular width. The thin blue lines represent individual predictions. The dashed curved lines represent credible intervals for 50, 80, and
95% probability. 20° n=40; 30° n=43; 40° n=41; 50° n=52; 60° n=42; 70° n=40.
Journal of Experimental Biology • Accepted manuscript
Figure 4. Effects of stimulus width on speed and tortuosity. A. Stimulus size affected the duration of the experiments, with animals presented with a control stimulus (angular width = 0°; n=37) taking significantly longer to complete trials than animals presented with 30-70° visual stimuli (Mann-
Whitney U Test with Bonferroni correction for pairwise comparisons). B. Full tracked paths of animals presented with control (left), 20° (centre), and 70° (right) stimuli. Note that not all
Journal of Experimental Biology • Accepted manuscript experiments were available on video for tracking. C. Straightness of animal paths (the length of the mean vector of turning angles, used to measure the efficiency of a directed walk) was consistently above 0.95 for all experiments, but was significantly higher in experiments using a visual stimulus than a control stimulus (Mann-Whitney U Test with Bonferroni correction for pairwise comparisons).
D. Sinuosity (a function of the mean cosine of turning angles, used to measure tortuosity in random walks) was significantly lower in experiments using a 70° than a control stimulus (Tukey’s test with
Bonferroni correction for pairwise comparisons). Asterisks indicate statistically significant differences
(padj<0.05).
Journal of Experimental Biology • Accepted manuscript
Figure 5. Ophiomastix wendtii does not respond to low-contrast vertical bar stimuli. A vertical bar stimulus of 60° angular width was also presented with Michelson’s contrasts of 0.05 (n=39) and 0.1
(n=42). A. Terminal bearings were disoriented relative to the centre of the stimulus. Arrows indicate the direction and length of the mean vector; blue brackets indicate maximum likelihood-based confidence intervals. B. Marginal effects at the mean of Michelson contrast as a categorical variable on rates of successful orientation for a control stimulus (MC=0, n=37) and three experimental stimuli
(MC of 0.05, 0.1 and 0.95). A circle represents a point estimate of the mean for each contrast level and a vertical line encloses the range of success proportions wherein the mean has 0.95 probability of falling.
Journal of Experimental Biology • Accepted manuscript
Figure 6. Orientation to a vertical bar stimulus is impaired in Ophiomastix wendtii missing a single arm (n=29). A. Terminal bearings relative to the initial orientation of the missing arm demonstrate that animals tend to move directly away from their missing arm. B. Individuals missing one arm did not orient to the centre of a stimulus of 60° angular width and Michelson contrast of 0.95 when placed in the arena at a random orientation. C. When individuals that began these experiments with the missing arm facing the stimulus were removed (open circles), the remaining individuals clustered around the stimulus. D. Comparisons of initial and terminal body orientation showed that the position of the missing arm relative to the arena did not change during experiments, i.e. animals did not turn. Arrows indicate the direction and length of the mean vector; blue brackets indicate confidence intervals around these.
Journal of Experimental Biology • Accepted manuscript Tables
Table 1 Orientation experiments using intact animals and variable stimulus size and contrast.
Results of maximum likelihood analyses of relative exit bearings with orientation models after
Schnute and Groot (1992); ϕ represents mean direction, κ represents concentration from circ_MLE.
Bold indicates a rejection of disorientation. % Success gives the proportion of animals to locate the stimulus, compared to expectations for random chance (in brackets).
*As stimulus is absent, this uses an arbitrary 60° section of the arena.
**From Sumner-Rooney et al. (2020).
Stimulus n Best model Model type Concentration Rho % success
(ΔAICc=0) (ϕ1, ϕ2) (κ 1, κ2) (expected)
Control 37 M1 Uniform NA 0.13 16.2 (16.7)*
20° 40 M1 Uniform NA 0.15 7.5 (5.6)
30° 43 M1 Uniform NA 0.12 13.9 (12)
40° 41 M1 Uniform NA 0.17 12.2 (11.1)
50°** 52 M4B Bimodal (177.3°, 357.3°) 0.174, 45.624 0.21 34.6 (13.9)
60° 42 M2A Unimodal (7.05°) 0.745 0.35 26.2 (16.7)
70° 40 M2B Unimodal (358°) 4.022 0.34 40 (19.4)
60° 42 M1 Uniform NA 0.06 21.4 (16.7)
(MC=0.1)
60° 39 M1 Uniform NA 0.13 20.5 (16.7)
(MC=0.05)
Journal of Experimental Biology • Accepted manuscript Table 2 Straightness and sinuosity indices for full animal paths in response to vertical bar stimuli. Straightness indices approaching 1 reflect a straight line; sinuosity indices approaching 0 reflect the lowest tortuosity.
Stimulus (°) n Straightness (± se) Sinuosity (± se)
0 29 0.9603 (±0.0054) 0.8643 (±0.051) 20 32 0.9724 (±0.0032) 0.7191 (±0.039) 70 28 0.9764 (±0.0036) 0.6365 (±0.053)
Journal of Experimental Biology • Accepted manuscript Table 3 Orientation experiments in animals missing a single arm, using a stimulus of 60° width and
Michelson contrast of 0.95. Results of maximum likelihood analyses of relative exit bearings, direction of movement relative to the position of the missing arm, and change in body orientation.
Orientation models after Schnute and Groot (1992); ϕ represents mean direction, κ represents concentration from circ_MLE. Bold indicates a rejection of disorientation.
*Indicates the exclusion of five animals that started the experiment with the stimulus facing the missing arm.
Metric n Mean Rho Best model Model type
(ΔAICc=0) (ϕ)
Relative bearing 29 349° 0.2 M1 Uniform (NA)
Direction of movement 29 178° 0.38 M2B Unimodal (191°)
Change in orientation 29 355° 0.92 M2A Unimodal (0°)
Relative bearing* 24 341° 0.31 M2C Unimodal (349°)
Journal of Experimental Biology • Accepted manuscript Journal of Experimental Biology: doi:10.1242/jeb.236653: Supplementary information
Supplementary data
Bayesian probability
Orientation data were modelled as angles according to the von Mises distribution using the Bayesian probabilistic modelling language Stan (Carpenter et al. 2017) and the R package brms (Bürkner
2017). Parameters were estimated over 40 000 sampled draws in four chains using weakly informative priors. Convergence was assessed by inspection of Markov chains, Ȓ and Neff statistics, and posterior predictive checks were used to test model efficacy. Modelled data were then contrasted against control data (from Sumner-Rooney et al. 2020) to assess the probability that animals departed from random orientation. The proportion of the contrasted distributions greater than zero can be interpreted as the probability that the corresponding treatment is oriented.
Von Mises modelling of headings found that, compared to experimentally obtained control data from Sumner-Rooney et al. (2020), animals were unlikely to be oriented to stimuli of 40° and below, but were very likely oriented to 50° and 60° stimuli (p≥0.92, Table S1, Figure S4).
Von Mises modelling of headings found that animals were unlikely to be oriented to stimuli with 0.1 or 0.05 Michelson contrast (Table S1, Figure S4). Journal of Experimental Biology • Supplementary information Journal of Experimental Biology: doi:10.1242/jeb.236653: Supplementary information
Figure S1 Prior predictive plot used for psychometric modelling of threshold stimulus width. Blue lines are 5000 possible model fits produced using the prior information only for the psychometric function model. The range and concentration of fitted lines illustrate the prior bias. The priors were informed by prior knowledge of O. wendtii response robustness to visual stimuli (Sumner-Rooney et al., 2020). High response proportions (> 0.7) were very unlikely, as are those well below chance. The black dashed line represents the mostly likely proportion by random chance (0.167). Journal of Experimental Biology • Supplementary information Journal of Experimental Biology: doi:10.1242/jeb.236653: Supplementary information
Figure S2 Orientation of Ophiomastix wendtii to stimuli of variable angular width, collapsed to 0-
180°. Sumner-Rooney et al. (2020) proposed that animals might orient to the areas of highest local contrast, the internal black-white edge of the stimulus. Orientation data (0-360°, Figure 2) were collapsed to 0-180° to visually inspect this; animals do not appear to specifically cluster at this edge. Journal of Experimental Biology • Supplementary information Journal of Experimental Biology: doi:10.1242/jeb.236653: Supplementary information
Figure S3 Differences between initial heading and terminal bearing of animals presented with control, 20°, and 70° stimuli. A. The heading of tracked animals was measured as they crossed the perimeter of a superimposed circle (diameter 10 cm) at the centre of the arena. B. Initial headings were subtracted from terminal bearings (see Figure 3). The differences clustered around 0° for all three stimuli, indicating little change in direction during experiments. Arrows indicate the direction and length of the mean vector; blue brackets indicate confidence intervals around these. Journal of Experimental Biology • Supplementary information Journal of Experimental Biology: doi:10.1242/jeb.236653: Supplementary information
Figure S4 Comparisons of animal orientation modelled as von Mises distributions. Each curve represents modelled orientations to a single experimental stimulus. The vertical line at log(kappa)=0 represents animal orientation to a control stimulus (from Sumner-Rooney et al., 2020). The proportion of the area under each curve that overlaps with the control can be interpreted as the probability that the animals were disoriented. See Table S1. Journal of Experimental Biology • Supplementary information Journal of Experimental Biology: doi:10.1242/jeb.236653: Supplementary information
Figure S5 Contrast transfer function of square wavelet and sine signals at 30° width, showing the
Michelson contrast remaining when Gaussian filtered through varying acceptance angles (full width at half maximum of the angular sensitivity function). Greater contrast remains for the square wave, making it as visible as the sine with worse visual acuity. Journal of Experimental Biology • Supplementary information Journal of Experimental Biology: doi:10.1242/jeb.236653: Supplementary information
Table S1 Bayesian analyses of orientation and ambient light conditions during experiments.
Relative headings were modelled according to Von Mises (angular) distributions. Prob. oriented indicates the probability that animals are more concentrated than would be expected by chance, according to a Bayesian model (based on statistical contrast with control data from Sumner-Rooney et al. 2020). Mean solar irradiance during orientation experiments June-July 2019 and May 2017.
Compiled from mean irradiance measurements taken across a 180° view every 15 minutes from
10am-3:15pm on the days of the experiments. Data provided by the Physical Monitoring Program of the Smithsonian Tropical Research Institute. Bold indicates the rejection of disorientation by circ_MLE (main text, Table 1) for comparison.
*From Sumner-Rooney et al. (2020)
Stimulus n Prob. oriented Mean irradiance Standard deviation
(W m-2) (W m-2) (vs. control)
20° 40 0.19 409.09 260.66
30° 43 0.49 337.34 173.65
40° 41 0.74 482.46 314.79
50°* 52 0.95 269.42 146.32
60° 42 0.92 598.4 261.49
70° 40 0.74 68.98 31.21
60° (MC=0.1) 42 0.85 200.5 96.73
60° (MC=0.05) 39 0.72 686.78 125.89 Journal of Experimental Biology • Supplementary information